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Ferromagnetism is an iconic example of a first-order phase transition taking place in spatially extended systems and is characterized by hysteresis and the formation of domain walls. We demonstrate that an extended atomic superfluid in the presence of a coherent coupling between two internal states exhibits a quantum phase transition from a paramagnetic to a ferromagnetic state. The nature of the transition is experimentally assessed by looking at the phase diagram as a function of the control parameters, at hysteresis phenomena, and at the magnetic susceptibility and the magnetization fluctuations around the critical point. We show that the observed features are in good agreement with mean-field calculations. Additionally, we develop experimental protocols to deterministically generate domain walls that separate spatial regions of opposite magnetization in the ferromagnetic state. Thanks to the enhanced coherence properties of our atomic superfluid system compared to standard condensed matter systems, our results open the way toward the study of different aspects of the relaxation dynamics in isolated coherent many-body quantum systems.

In the injured spinal cord, chondroitin sulfate proteoglycans (CSPGs) are the principal responsible of axon growth inhibition and they contribute to regenerative failure, promoting glial scar formation. Chondroitinase ABC (chABC) is known for being able to digest proteoglycans, thus degrading glial scar and favoring axonal regrowth. However, its classic administration is invasive, infection-prone and clinically problematic. An agarose-carbomer (AC1) hydrogel, already used in SCI repair strategies, was here investigated as a delivery system capable of an effective chABC administration: the material ability to include chABC within its pores and the possibility to be injected into the target tissue were firstly proved. Subsequently, release kinetic and the maintenance of enzymatic activity were positively assessed: AC1 hydrogel was thus confirmed to be a feasible tool for chABC delivery and a promising device for spinal cord injury topic repair strategies.